A spatial-temporal model for temperature with seasonal variance

We propose a spatial-temporal stochastic model for daily average temperature data. First we build a model for a single spatial location, independently on the spatial information. The model includes trend, seasonality and mean-reversion, together with a seasonally dependent variance of the residuals. The spatial dependency is modelled by a Gaussian random field. Empirical fitting to data collected in 16 measurement stations in Lithuania over more than 40 years shows that our model captures the seasonality in the autocorrelation of the squared residuals, a property of temperature data already observed by other authors. We demonstrate with some examples that our spatial-temporal model is applicable for prediction and classification